Back to basics: historical option pricing revisited

We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments are uncorrelated (but not necessarily independent) and of arbitrary probability density. We discuss in particular how, in the Gaussian limit, the Black-Scholes results are recovered, including the fact that the average return of the underlying stock disappears from the price (and the hedging strategy). We compare this theory to real option prices and find these reflect in a surprisingly accurate way the subtle statistical features of the underlying asset fluctuations.Comment: 14 pages, 2 .ps figures. Proceedings, to appear in Proc. Roy. So

An Asymptotic Analysis of an American Call Option with Small Volatility N. P. Firth

this paper we present an asymptotic analysis of an American call option where the di#usion term (volatility) is small compared to the drift terms (interest rate and continuous dividend yield). We show that in the limit where di#usion is negligible, relative to drift, then, at leading order, the American call's behaviour is the same as a perpetual American call option (except in a boundary layer about the option's expiry date).